Effect of Scaling Parameters on Waterflood Performance with

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Energy & Fuels 2008, 22, 402–409

Effect of Scaling Parameters on Waterflood Performance with Horizontal and Vertical Wells Nanji J. Hadia,† Lalit S. Chaudhari,† Sushanta K. Mitra,*,† Madhu Vinjamur,‡ and Raghuvir Singh§ IITB-ONGC Joint Research Centre, Indian Institute of Technology Bombay, Powai, Mumbai, India 400 076 ReceiVed February 22, 2007. ReVised Manuscript ReceiVed August 10, 2007

This paper presents numerical study on the effect of scaling parameters on the waterflood performance with different well configurations. The oil recoveries obtained from experiments on a laboratory scale model have been compared with those obtained from a model, which is scaled up using scaling relationships which are in the form of dimensionless numbers. The effects of dimensionless scaling groups like effective aspect ratio, mobility ratio, buoyancy number, and capillary number on breakthrough oil recovery (BOR) with four different well configurations, viz., vertical injection-vertical production (VI-VP), vertical injection-horizontal production at top (VI-HPT), vertical injection-horizontal production at bottom (VI-HPB), and horizontal injection at bottomhorizontal production at top (HIB-HPT), are reported. It is found that the HIB-HPT well configuration gives higher oil recovery and that VI-HPB gives lower recovery than other well configurations under most of the conditions considered. For higher buoyancy numbers, all configurations result in lower BOR values except VI-HPT, which leads to a higher BOR. However, the performance of other well configurations is also comparable to that of HIB-HPT under certain conditions.

Introduction The displacement of one fluid by another in a porous medium is the basis for any oil recovery process. Large quantities of oil remain trapped after primary recovery. Further recovery of oil is possible by secondary and/or tertiary recovery processes. During secondary recovery process, water injected through an injection well displaces oil out through a production well. This process is known as waterflooding which falls under the category of immiscible displacement processes and is the most widely used secondary recovery process. Traditional waterflooding is done with various patterns of injection and production wells—both of which are vertical. But since the last two decades, the petroleum industry has experienced a rapid increase in use of horizontal wells for oil recovery processes. For a typical reservoir, the height is small compared to length and width. Hence, horizontal wells offer a larger contact area than vertical wells and may lead to higher production rates, sometimes as large as 2-5 times.1 Application of horizontal wells for oil recovery are found in waterflooding,2 thermal recovery,3–5 chemical and polymer flooding,6 steam-CO2 drive experiments,7immiscible CO2 and WAG injection,8 etc. Most of these studies have shown that the horizontal wells improve the ultimate oil recovery over that * Corresponding author. Phone: +91 (22) 2576 4521. Fax: +91 (22) 2572 6875. E-mail: [email protected]. † Department of Mechanical Engineering, IITB. ‡ Department of Chemical Engineering, IITB. § Institute of Reservoir Studies, ONGC, Ahmedabad, India. (1) Joshi, S. D. J. Pet. Technol. 1988, 729–739. (2) Taber, J. J.; Seright, R. Horizontal Injection and Production Wells for EOR or Waterflooding. Presented at the 1992 SPE Permian Basin Oil and Gas Recovery Conference, Midland, TX, March 18–20, 1992; paper SPE 23952. (3) Joshi, S. D. A Laboratory Study of Thermal Oil Recovery Using Horizontal Wells. Presented at fifth Symposium on EOR of SPE and DOE, Tulsa, OK, Apr 20–23, 1986; paper SPE/DOE 14916. (4) Bagci, S.; Gumrah, F. J. Pet. Sci. Eng. 1992, 8, 59.

of conventional vertical wells. The reasons for increase in the use of horizontal wells over vertical wells are due to the following: (i) productivity (production rate per unit pressure drop of the reservoir), (ii) intersection with and drainage of verticalfracture networks, (iii) reduction of gas and water coning, and (iv) increase in sweep efficiency.9 We consider waterflooding only in this work. To predict recovery performance in a reservoir, the traditional practice is to make oil recovery experiments on a laboratory scale model of the reservoir. The data obtained from this model can be correlated to recovery from the reservoir with the help of scaling relationships or scaling laws. The objective of scaling is to produce a one-to-one relationship between the physical and dynamic characteristics/behavior of the model and the prototype. Scaling generally leads to nondimensional numbers known as dimensionless scaling groups. When these groups are same for both a model and a prototype, then the two will likely behave in a similar manner. There are two methods used to derive the dimensionless scaling groups, which are dimensional analysis and inspectional analysis. The former is based on the information of the relevant variables involved in the displacement process. The latter is stronger since it is based on the underlying physical laws, usually expressed in the form of differential equations and initial and boundary conditions.10 (5) Guanghul, Z.; Zhang, R.; Shen, D.; Pu, H. Horizontal Well Application in High Viscous Oil Reservoirs. Presented at the International Heavy Oil Symposium, Calgary, Alberta, Canada, June 19–21, 1995; paper SPE 30281. (6) Bagci, S.; Hodaie, H. Energy Sources 2003, 25, 253. (7) Gumrah, F.; Bagci, S. J. Pet. Sci. Eng. 1997, 18, 113. (8) Erdal, T.; Bagci, S. J. Pet. Sci. Eng. 2000, 26, 67. (9) Babu, D. K.; Odeh, A. S. J. Pet. Technol. 1989, 914–915. (10) Shook, M.; Li, D.; Lake, W. In-Situ 1992, 16 (4), 311. (11) Leverett, M. C.; Lewis, W. B.; True, M. E. Trans. AIME 1942, 175–193.

10.1021/ef070097b CCC: $40.75  2008 American Chemical Society Published on Web 11/27/2007

Waterflooding with Horizontal and Vertical Wells

Several papers reported the use of scaling laws for petroleum recovery processes. Leverett et al.11 initiated the study of oil field behavior using dimensionally scaled models. They concluded that the viscosity of liquids used in the model and the permeability of model should be much higher than that of the reservoir. Rapoport12 presented for the first time an inspectional analysis to come up with scaling relationships of immiscible displacement of oil by water. Geertsma et al.13 later extended the work of Rapoport12 by including the hot water and solvent displacement. They used both inspectional and dimensional analysis for the derivation of dimensionless groups. A detailed scaling study by Croes and Schwarz14 reported the effect of oil/water viscosity ratio on immiscible displacement of oil by water. Craig et al.,15 in their scaling study, correlated the results of model studies with mobility ratio rather than the viscosity ratio. Carpenter et al.16 presented the results of model studies to demonstrate the validity of scaling relationships of Rapoport12 to water-wet reservoirs with communicating layers of different permeability. Perkins and Collins17 presented a set of scaling criteria which permits different relationships between saturation and relative permeability and capillary pressures in the model and the prototype. Using inspectional analysis, van Daalen and van Domslaar18 studied the scaling of models that have different geometries from that of the prototype. They showed that the aspect ratio is not important in scaling for immiscible displacements where there is no crossflow in the reservoir. Shook et al.10 carried out a rigorous inspectional analysis for scaling immiscible displacements in porous media. They showed that the scaling of the immiscible displacement problem requires the matching of six dimensionless groups. In addition, petrophysical properties should also match for the model and the prototype. Peters et al.19 carried out an extensive study of scaling unstable immiscible displacement in porous media. Their results indicate that unstable immiscible displacements in water-wet media are more efficient than those in oil-wet media. Also, Li and Lake20 presented scaled results of immiscible displacement of oil by water in two-dimensional, anisotropic, heterogeneous reservoirs with vertical wells. They concluded that having scaling groups of matching heterogeneity gives statistically identical dimensionless results between different heterogeneous systems. Gharbi21 presented a general method to scale flow through heterogeneous reservoirs for miscible displacement of oil by a solvent. Through inspectional analysis, he showed that scaling miscible displacements in two-dimensional, heterogeneous, anisotropic medium requires the matching of 13 dimensionless scaling groups. Recently, Algharaib et al.22 presented a numerical study for homogeneous reservoirs with horizontal wells with a range of the nondimensional scaling groups. The authors revealed in detail the conditions under which a particular well (12) Rapoport, L. A. Trans. AIME 1955, 204, 143. (13) Geertsma, J.; Croes, G. A.; Schwarz, N. Trans. AIME 1956, 207, 118. (14) Croes, G. A.; Schwarz, N. Trans. AIME 1957, 204, 35. (15) Craig, F. F.; Sanderlin, J. L.; Moore, D. W.; Geffen, T. M. Trans. AIME 1957, 210, 275. (16) Carpenter, C. W.; Bail, P. T.; Bobek, J. E. SPE J. 1962, 9–12. (17) Perkins, F. M.; Collins, R. E. J. Pet. Technol. 1960, 69–71. (18) Van Daalen, F.; van Domslaar, H. R. SPE J. 1972, 12, 220. (19) Peters, E. J.; Nadeem, A.; Gharbi, R. J. Pet. Sci. Eng. 1993, 9, 183. (20) Li, D.; Lake, L. W. SPE AdV. Technol. Ser. 1996, 3 (1), 188. (21) Gharbi, R. Trans. Porous Media 2002, 4 (2), 113. (22) Algharaib, M.; Gharbi, R.; Malallah, A. Trans. Porous Media 2006, 65, 89.

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configuration may lead to better oil recovery for a given combination of dimensionless groups. Though a lot of literature is available on the scaling aspects of oil reservoirs and different recovery processes, there are only a few reports on the effect of the scaling groups on the oil recovery during waterflooding. The present study reports a numerical simulation study on the effect of various dimensionless scaling groups on breakthrough oil recovery with different vertical and horizontal well configurations. Moreover, a verification exercise for scaling groups has been carried out by simulating the prototype using scaling parameters corresponding to the laboratory experiments performed by Hadia et al.23 A good agreement between oil recoveries obtained from the model and the prototype provoked us to study the effect of scaling parameters on the performance of a reservoir with different configurations of vertical and horizontal wells. In what follows, dimensionless numbers reported by Shook et al.10 are mentioned. Then, the validation of the numbers by comparison between model and prototype is discussed. Then, the effect of the numbers on breakthrough oil recovery (BOR) with different well configurations is explained on the basis of simulations by the commercial software ECLIPSE100.24 Dimensionless Scaling Groups For an immiscible displacement of oil by water in a reservoir, the following are the important dimensionless scaling groups which must be the same in order to have the same performance of the model and the prototype:10 Effective aspect ratio, RL ) Mobility ratio, M )

L H

Kv Kh

Krw µo Kro µw

Buoyancy number, NB ) Capillary number, NC )

KhKro∆Fg uTµo uTµoL Kroσ√φKh

(1) (2) (3) (4)

In the above equations, L is length; H is height; and Kv and Kh are vertical and horizontal permeabilities of porous medium, respectively. Kro and Krw are end-point relative permeabilities; and µo and µw are viscosities, of oil and water, respectively. ∆F is the density difference, and σ is the interfacial tension between water and oil. Here, φ is the porosity, and g represents the acceleration due to gravity. Also, uT is average fluid velocity in the porous medium and can be calculated by dividing the injection rate by porosity times the cross-sectional area open to the flow at the midplane between the vertical injection and production wells. The mobility ratio, M, indicates the relative ease with which the oil and water phases flow. A higher mobility ratio implies that water flows easily, and a low mobility ratio indicates that oil flows easily. The effective aspect ratio includes the effect of the ratio of the vertical to horizontal permeability and reservoir dimensions. Buoyancy number, NB, is the ratio of gravity force to viscous force in an immiscible displacement in the porous media. Higher NB values indicate a higher gravity force or the reduced influence of viscous force on the fluid flow (23) Hadia, N.; Chaudhari, L.; Mitra, S. K.; Vinjamur, M.; Singh, R. Energy Sources, Part A 2006, in press. (24) ECLIPSE Reference Manual 2005A; GeoQuest, Schlumberger Inc.: Houston, TX, 2005.

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Table 1. Data for ECLIPSE Simulation parameter length of model width of model depth of model porosity, % horizontal permeability (Kh), mD horizontal to vertical permeability ratio water viscosity, cP oil viscosity, cP water density, gm/cc oil density, gm/cc Kro Krw injection rate buoyancy number, NB effective aspect ratio, RL mobility ratio, M

laboratory model23 30 cm 30 cm 10 cm 20.9 1500 10 0.97 130 1 0.82 1 0.027 60 cc/h 0.006 0.95 3.62

field 150 m 150 m 50 m 20.9 1500 10 0.6 80 1 0.9 1 0.027 354 m3/d 0.006 0.95 3.62

in the reservoir. This condition most likely occurs when the oil viscosity and injection rates are low. The capillary number, NC, is the ratio of capillary to viscous forces and is a measure of the influence of capillary forces on the displacement process. The capillary forces are dominant at low displacement rates and in the case where the wetting phase displaces the nonwetting phase. Results and Discussion The experimental results of Hadia et al.23 have been considered for the validation of the scaling groups. The scale ratio of 500 has been chosen between the physical dimensions of the model and the reservoir. The experimental parameters for the laboratory model and the corresponding field prototype parameters are provided in Table 1. From the mobility ratio with assumed water viscosity, the reservoir oil viscosity has been calculated. The field water injection rate has been calculated by assuming the buoyancy number to be the same in both the model and the prototype. The commercial simulator, ECLIPSE100,24 is used to perform the simulation study. ECLIPSE100 is a fully implicit, finite difference, three-phase, three-dimensional, black oil simulator. The field reservoir is modeled by means of Cartesian grid geometry with the number of grids in X, Y, and Z directions being 50, 50, and 17, respectively. It is to be noted that, for field scale simulation, the same relative permeability curve has been used as that obtained for the laboratory model and capillary pressure is assumed to be negligible. Also, the fluids are assumed to be incompressible. The experimental results of laboratory experiments are then compared with those obtained from field scale simulations. Figure 1 shows the comparison of oil recoveries for three different well configurations (vertical injection-vertical production (VI-VP), vertical injection-horizontal production at top (VI-HPT), and vertical injectionhorizontal production at bottom (VI-HPB)), and they match closely. The field scale simulations have been performed by changing different inputs in the mobility ratio, buoyancy number, and effective aspect ratio such that their values remain same. The parameters varied are horizontal permeability (500-3000 mD), vertical permeability (50-300 mD), length (100-250 m), and water viscosity (0.6-1 cP). The simulation results thus obtained are found to be in close agreement with the experimental results.23 This good agreement motivated us to study the effect of various dimensionless numbers, defined before, on breakthrough oil recovery (BOR) from a laboratory scale model by simulations. We believe that the results of these simulations are applicable to prototypes scaled up appropriately.

Figure 1. Comparison of recoveries obtained from experiments23 and simulation for (a) VI-VP, (b) VI-HPT, and (c) VI-HPB well configurations. Dots and solid lines indicate experiments and simulations, respectively.

Numerical Analysis. A numerical simulation study has been carried out to investigate the effect of the dimensionless scaling groups and waterflood performance with vertical and horizontal well configurations. The prototype is considered to be horizontal, three-dimensional, and homogeneous and represents a quarter of a five-spot pattern with vertical and horizontal wells placed inside it. Four different well configurations, as shown in Figure 2, are considered for this purpose. They are the following: (i) vertical injection-vertical production (VI-VP), (ii) vertical injection-top horizontal production (VI-HPT), (iii) vertical injection-bottom horizontal production (VI-HPB), and (iv) horizontal injection-



Figure 2. Well configurations considered in numerical simulations: (a) VI-VP, (b) VI-HPT, (c) VI-HPB, and (d) HIB-HPT well configurations.

Figure 3. Effect of buoyancy number on breakthrough recovery from waterflooding for (a) HIB-HPT, (b) VI-VP, (c) VI-HPB, and (d) VI-HPT well configurations. The capillary number is set to zero, and the effective aspect ratio, to 1.0.

horizontal production (HIB-HPT). It is to be noted that all the wells are assumed to be fully perforated along their lengths. Figure 3 shows the effects of buoyancy number (NB) on breakthrough oil recovery (BOR) for three different mobility ratios for all well configurations. The aspect ratio, RL, is maintained at a constant value of unity, and the capillary number is assumed to be zero in all the cases. It can be observed from Figure 3 that, in general, as the mobility ratio increases, the BOR decreases in all well configurations. With the rise in

mobility ratio, the swept area and volume fall with a concomitant fall in BOR. It is to be noted that, from this figure onward, the X coordinate of all the plots is logarithmic. Figure 3a shows that with the HIB-HPT well configuration, the BOR for a low value of mobility ratio (M ) 0.1) remains nearly same for the range of buoyancy number considered. However, for M ) 1, a small decrease in BOR is observed for NB > 1. With a rise in the mobility ratio, the swept area remains more or less same with increasing NB with a marginal decrease


Hadia et al.

Figure 4. Waterflood saturation profiles at breakthrough at NB ) 0.5 and 10 for (A) VI- HPT and (B) VI-VP well configurations at (a) top plane, (b) middle plane, and (c) bottom plane. The effective aspect ratio is maintained at 1, and the mobility ratio, at 1.

at higher NB values. Unlike for the HIB-HPT configuration, BOR decreases as NB increases for VI-VP well configurations (Figure 3b). For M ) 0.1, the BOR decreases sharply around NB ) 1. With increase in NB, water tends to be at the bottom and will issue out of production well results in reduced BOR. For higher mobility ratios, the BOR falls at the lower NB because of difficulty in displacing oil. Figure 3c shows the relationship of the waterflood BOR with NB for a reservoir with the VI-HPB well configuration. The performance is similar to that of the VI-VP configuration for M ) 0.1 but with decrease in BOR. The placement of the horizontal production well at the bottom of the reservoir results in the lowest BOR among all the well configurations.

Figure 3d shows the breakthrough recovery performance as a function of NB for a reservoir with the VI-HPT well configuration. In general, it is observed that BOR increases with NB. The value of NB at which the increase in BOR commences is, however, different for all the mobility ratio values. The increase in BOR with increase in NB is mainly attributed to the increased effect of gravity forces over the viscous forces due to which water has a propensity to settle down at the bottom. This results in an increased content of oil on the top of the reservoir. As the horizontal well is placed at the top of the reservoir, the water breakthrough is delayed resulting in higher BOR. Figure 4shows the simulation oil saturation profiles at breakthrough for the VI-HPT and VI-VP configurations at



Figure 5. Effect of buoyancy number on breakthrough recovery from waterflooding for (a) HIB-HPT, (b) VI-VP, (c) VI-HPB, and (d) VI-HPT well configurations. The capillary number is set to zero, and the mobility ratio, to 0.1.

buoyancy numbers of 0.5 and 10.0. For each figure, the oil saturation at the top, middle, and bottom planes are shown and are labeled as a, b, and c, respectively. It can be observed from Figure 4AI that, at a buoyancy number of 0.5, the waterflood front movement is uniform from the top to the bottom plane of the reservoir which indicates that the gravity effects are negligible. At a buoyancy number of 10.0, however, there is a decrease in oil saturation from the top to the bottom plane as shown in Figure 4AII. This is attributed to the predominant effect of gravity forces over viscous forces in the reservoir at high buoyancy numbers. Since the horizontal production well is placed at the top of the reservoir, this results in higher breakthrough recovery in the case of the VI-HPT configuration. Figure 4BI shows that at a buoyancy number of 0.5 (viscous dominated reservoir), the flood front movement is uniform throughout the reservoir and hence a higher sweep area in the case of the VI-VP well configuration finally results in higher BOR. For a buoyancy number of 10.0, however, due to predominant effect of gravity forces, the oil saturation decreases from the top to the bottom of the reservoir as shown in Figure 4BII, resulting in low BOR. Figure 5 shows the functional relationship between NB and BOR at three different values of the effective aspect ratio (RL) for all the well configurations. In all the cases, the capillary pressures are assumed to be zero and mobility is maintained at a value of 0.1. It can be observed from Figure 5a that, with the HIB-HPT well configuration, the BOR remains almost constant

for the range of NB values considered. This is mainly attributed to the fact that as the horizontal injection well is placed at the bottom and the production well is at the top of the reservoir, and is fully penetrating the reservoir, the sweep area remains almost same at all buoyancy numbers. This results in negligible change in the BOR with increase in NB. Moreover, from Figure 5a, it can also be observed that there is a marginal increase in BOR with increase in RL. For thin reservoirs, the value of RL is high, and for such reservoirs with a horizontal injection well at the bottom and the production well at the top, the area swept is higher, and hence, higher BOR results. Figure 5b shows that BOR increases with a decrease in RL for the VI-VP well configuration for low buoyancy numbers. That is, for thin reservoirs (high RL), the VI-VP configuration leads to less oil recovery. The contact area as well as the swept area and volume are lower for thin reservoirs with the VI-VP configuration, and hence, BOR decreases. It is also observed that for high RL (RL ) 10), the BOR remains more or less constant for the range of buoyancy number considered which is due to the negligible gravity forces in thin reservoirs. For thick reservoirs (RL ) 0.1), however, the BOR decreases sharply around the value of NB ) 1 which indicates the predominant gravity effects in thick reservoirs. Figure 5c and d shows the effect of buoyancy number on waterflood performance for the VI-HPB and VI-HPT well configurations, respectively. It can be observed, in general, from both the figures that as the value of effective aspect ratio


Hadia et al.

Figure 7. Effect of buoyancy number on breakthrough recovery from waterflooding with four different well configurations with mobility ratios of (a) M ) 0.1 and (b) M ) 1. The capillary number is set to zero, and the effective aspect ratio, to 10.

Figure 6. Effect of buoyancy number on breakthrough recovery from waterflooding with four different well configurations with mobility ratios of (a) M ) 0.1, (b) M ) 1, and (c) M ) 10. The capillary number is set to zero, and the effective aspect ratio, to 1.

increases, the breakthrough oil recovery increases. It is also observed that the BOR remains nearly constant in both the cases until NB is unity. For NB > 1, however, an opposite trend is observed for both the well configurations. With the VI-HPB well configuration, there is a decrease of the BOR for NB > 1, and with the VI-HPT well configuration, the BOR increases. It is also observed from Figure 5c and d that for the case of RL ) 10 (thin reservoirs), the BOR remains constant for the range of buoyancy number considered. This indicates that, for thinner reservoirs, the placement of the horizontal production well has no effect on the breakthrough oil recovery. The comparison of the effect of the buoyancy number on the BOR for all well configurations are shown in Figure 6 for different mobility ratios of 0.1, 1, and 10. The effective aspect ratio is maintained at 1, and the capillary number is assumed to be zero for all cases. In general, it can be observed from Figure 6 that VI-HPB gives the least BOR and that HIB-HPT gives the highest among all well configurations.

It is observed from Figure 6a that, for the VI-VP, VI-HPT, and HIB-HPT well configurations, for the viscous dominated region (NB < 1), the BOR does not change significantly. However, for the VI-VP and VI-HPB well configurations, the BOR decreases when NB > 1 which can be attributed to the dominance of gravity forces over viscous forces. For the HIBHPT well configuration, however, there is no significant effect of gravity on the BOR over the range of buoyancy number considered. It is also important to note that for viscous dominated reservoirs (NB < 1), the VI-VP and HIB-HPT well configurations perform equally well, whereas for gravity dominated reservoirs (NB > 1), the performance of the VI-HPT well configuration is comparable to that of HIB-HPT. From Figure 6b and c, it can be noted that the performance of a well configuration at mobility ratios of 1.0 and 10.0 is similar to its performance at a lower mobility ratio of 0.1 (Figure 6a) but with decrease in BOR. High mobility ratios reduce the displacement efficiency leading to lower BOR. The comparison of the waterflooding performance for all well configurations for mobility ratios of 0.1 and 1 with an effective aspect ratio of 10 is shown in Figure 7. The capillary number is assumed to be zero for both the cases. It is observed from Figure 7a that, for thin reservoirs with a very low mobility ratio of 0.1, all well configurations except VI-VP produce the same BOR in viscous dominated reservoirs (NB < 1). For gravity dominated reservoirs (NB > 1), the decrease of the BOR is observed for the VI-HPB and VI-VP configurations. The reduced BOR for the VI-VP configuration in a thin reservoir is because of having less reservoir contact area of vertical wells. Moreover, it is also observed that for highly gravity dominated



Figure 8. Effect of capillary number on the breakthrough recovery from waterflooding for the (a) HIB-HPT, (b) VI-VP, (c) VI-HPB, and (d) VI-HPT well configurations. The effective aspect ratio is set to 1, and the mobility ratio, to 0.1.

waterfloods (NB ) 10), the VI-VP and VI-HPB well configurations produce nearly the same breakthrough recovery. Figure 7b shows the waterflooding performance for all well configurations with reservoir conditions of RL ) 10, M ) 1, and NC ) 0. The results follow the similar trend, for the VI-VP and VIHPB well configurations, as observed in the case with RL ) 1 (Figure 7a). However, for the VI-HPT and HIB-HPT well configurations, in gravity dominated reservoirs (NB > 1), unlike the case with M ) 0.1, breakthrough recovery decreases with increase in the buoyancy number. Figure 8 shows the combined effect of capillary number, NC, and the buoyancy number, NB, on the waterflood breakthrough recovery for all the well configurations. Since NC represents the ratio of capillary to viscous forces and NB represents the ratio of gravity to viscous forces, Figure 8 shows the interplay of the three important forces and its effect on the oil recovery. The results are shown for three different buoyancy numbers 0.02, 0.1, and 1. The general observation for a well configuration is that for the buoyancy numbers considered, the BOR increases with increase in NC up to the value of 10 and then becomes independent of it. Moreover, with increase in the buoyancy number, the BOR decreases at lower values of NC for all well configurations. Conclusions A comprehensive numerical simulation study has been carried out to investigate the effect of scaling parameters on waterflood

oil recovery with different vertical and horizontal well configurations. The scaling parameters have been validated with the available experimental results. From the numerical simulation analysis, the following conclusions can be made: (1) The recovery performance of the HIB-HPT well configuration seems to be the highest, and that of VI-HPB seems to be the lowest among all well configurations. (2) For thick reservoirs in the viscous dominated region, however, the VI-VP configuration is equally effective as HIBHPT. For gravity dominated reservoirs (higher NB), the waterflood recovery from HIB-HPT and VI-HPT is comparable. This is true for reservoirs with negligible capillary pressures. (3) For thin reservoirs (with a high aspect ratio) at a low mobility ratio, the performance of all well configurations is comparable in the viscous dominated region. At high mobility ratios, HIB-HPT and VI-HPT perform better in both viscous and gravity dominated regions. (4) Capillary pressure tends to reduce the recovery performance of a reservoir for all well configurations. Acknowledgment. We would like to thank the Institute of Reservoir Studies (IRS), Ahmedabad (India), a subsidiary of the Oil and Natural Gas Corporation (ONGC) Ltd., for financial support through Contract No. IRS/IITB/F&NM/2004/1 and Schlumberger Inc. for providing the ECLIPSE numerical simulator. EF070097B

Effect of Scaling Parameters on Waterflood Performance with

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